Question

Table 4

            Regression Model

            Y = α X1 + β X2

            Parameter Estimates

                                    Coefficient        Standard Error

            Constant               12.924                  4.425

            X1                         -3.682                 2.630

            X2                        45.216                12.560

            Analysis of Variance

            Source of         Degrees            Sum of             Mean

            Variation           of Freedom       Squares            Square             F

            Regression       XXX                 4,853                2,426.5             XXX

            Error                 XXX                 485.3

  1.    Find above partial statistical output based on a sample of 16 observations presented in Table 4.  
         The dependent variable is called Y. There are two independent variables, X1 and X The notation ‘XXX’
         indicates that the information is omitted from Table 4. Use this information to answer the following questions.
  1. Interpret the coefficient on X1. To be specific, what is the impact of a one unit change of X1 on Y?
  2. What is the value of the corresponding test statistic to test that coefficient on X1 is significantly different from zero? (Round the value of the test statistic to two decimal places.)
  3. What is the correct statistical decision for the test of whether the coefficient on X1 is significantly different from zero using the rule of thumb that the t test statistic should be bigger than 2? In you answer, use the correct terminology for a statistical decision: “Reject the Null Hypothesis” or “Fail to Reject the Null Hypothesis.”
  4. Interpret the coefficient on X2. To be specific, what is the impact of a one unit change of X2 on Y?
  5. What is the value of the corresponding test statistic to test that coefficient on X1 is significantly different from zero? (Round the value of the test statistic to two decimal places.)
  6. What is the correct statistical decision for the test of whether the coefficient on X2 is significantly different from zero using the rule of thumb that the t test statistic should be bigger than 2? In you answer, use the correct terminology for a statistical decision: “Reject the Null Hypothesis” or “Fail to Reject the Null Hypothesis.”
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